Question

Sum of three terms in GP is 13 /12 and product is -1. Find the Gp​

Answer 1

$<u> <b> Heya !! </u>$

$<u> Geometric Progressions </u>$

The sum of the first three terms of a G.P is 13/12 and their product is -1 . Find the common ratio and the terms .

Ans.→ Let us assume that the terms are :- a , a/r and ar

Given that ,

$= > ar + \frac{a}{r} + a = \frac{13}{12}$

Also ,

=> a × ar × a/r = -1

=> a³ = -1

°•° The first term a = -1 ✔

Substituting the value of a , we have the equation ,

$= > - r - \frac{1}{r} - 1 = \frac{13}{12}$

↑ Solving this we will get a quadratic equation [ of the form ax² + bx + c ]

=> 12r² + 25r + 12

=> 12r² + 16r + 9r + 12 [ splitting middle.term]

=> 4r ( 3r + 4 ) +3 ( 3r + 4)

=> ( 4r + 3) (3r + 4)

•°• r = -¾ or r = - 4/3

Terms are 4/3 , -1 and 3/4 [ for r = -3/4]

Terms are 3/4 , -1 and 4/3 [ for r = -4/3]

Thanks!!

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Answer 2

Answer:

Step-by-step explanation:

let first term be a/r

second be a

and third be ar

.acc to que.-

a/r+a+ar=13/12

a+ar+ar^2/r=13/12

Now u will solve